I suppose you're referring to a Riemann sum.
Using the right endpoint method,
Since a=0, we have
Sub into what is to be integrated:
The thing to do here is to write the sum in terms of n.
The sum of the first n fourth powers is given by:
So, you get:
Expand out and take the limit as
You should get your answer the same as if you integrated the 'quick' way.